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A model of memristor-based Chuas oscillator is studied. The considered systemhas infinitely many equilibrium points, which build a line of equilibria.Bifurcational mechanisms of oscillation excitation are explored for differentforms of nonlinearity. Hard and soft excitation scenarios have principallydifferent nature. The hard excitation is determined by the memristorpiecewise-smooth characteristic and is a result of a border-collisionbifurcation. The soft excitation is caused by addition of a smooth nonlinearfunction and has distinctive features of the supercritical Andronov-Hopfbifurcation. Mechanisms of instability and amplitude limitation are describedfor both two cases. Numerical modelling and theoretical analysis are combinedwith experiments on an electronic analog model of the system under study. Theissues concerning physical realization of the dynamics of systems with a lineof equilibria are considered. The question on whether oscillations in suchsystems can be classified as the self-sustained oscillations is raised.

Hard and soft excitation of oscillations in memristor-based oscillators with a line of equilibria